In exploration geophysics, different seismic migration imaging methods, such as reverse time migration (RTM), one-way wave-equation migration, and ray-based migration, are used to map observed seismic data to subsurface true reflectivity positions using the given velocity model in order to obtain the reliable subsurface images for interpretation. Such a process of mapping seismic data to subsurface earth model is called seismic migration.
Seismic migration can be considered as adjoint of seismic forward modeling. Seismic modeling under the Born approximation is approximated as a weighted summation of the Green's function. In matrix form, it can be expressed as d=Gm, in which d is acquired seismic data, m is subsurface earth model, G is modeling operator related to acquisition geometry and earth physical property. The migration image m′ is computed by applying the adjoint G′ of the forward modeling operator G to the acquired seismic data, m′=G′d=G′Gm. If G′G is not an identity matrix, m′ is not the same as m, which means that migrated image m′ is a blurred version of true earth model representation. G′G is the blurred matrix related to the limitations in seismic data acquisition aperture, limited seismic imaging aperture, coarse acquisition geometry, etc. The migrated image often contains numerical artifacts or noises. These migration artifacts pollute and degrade seismic image quality, leading to low image resolution and poor image illumination in complex structure area.
Numerous methods have been proposed to address these issues. Two of the commonly used methods are iterative least squares migration and deblur or point spread function (PSF) deconvolution. PSF is also called a blurring kernel. Both these technologies are capable of improving the resolution and suppress acquisition footprints in migrated images or migration artifacts efficiently. Instead of solving for the exact inverse of G′G. PSF deconvolution computes a relatively inexpensive approximation to the inverse of G′G. The drawback of the least squares migration is its high computational cost due to its implementation in an iterative manner. The PSF deconvolution is non-iterative method that is able to reduce migration artifacts efficiently. However, it suffers from instability because of ill-condition in constructing filtering operator.
In reality, the subsurface medium is usually anisotropy. The current isotropic migration deconvolution is not appropriate to handle complex media where there is anisotropy. The current disclosure proposes a new method to build matching filtering operator based on anisotropy modeling and migration engine. The proposed method employs the step of matching filtering. Because the anisotropy propagation engine is used for constructing matching filtering matrix, the new method is an anisotropy matching filtering algorithm for seismic migration artifact attenuation. Synthetic data test results demonstrate its capability of improving the energy focusing and illumination.